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Java example source code file (SphericalCoordinatesTest.java)

This example Java source code file (SphericalCoordinatesTest.java) is included in the alvinalexander.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Java by Example" TM.

Learn more about this Java project at its project page.

Java - Java tags/keywords

derivativestructure, dimensionmismatchexception, sphericalcoordinates, sphericalcoordinatestest, test, vector3d

The SphericalCoordinatesTest.java Java example source code

/*
 * Licensed to the Apache Software Foundation (ASF) under one or more
 * contributor license agreements.  See the NOTICE file distributed with
 * this work for additional information regarding copyright ownership.
 * The ASF licenses this file to You under the Apache License, Version 2.0
 * (the "License"); you may not use this file except in compliance with
 * the License.  You may obtain a copy of the License at
 *
 *      http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */

package org.apache.commons.math3.geometry.euclidean.threed;

import org.apache.commons.math3.TestUtils;
import org.apache.commons.math3.analysis.differentiation.DerivativeStructure;
import org.apache.commons.math3.exception.DimensionMismatchException;
import org.apache.commons.math3.util.FastMath;
import org.junit.Assert;
import org.junit.Test;

public class SphericalCoordinatesTest {

    @Test
    public void testCoordinatesStoC() throws DimensionMismatchException {
        double piO2 = 0.5 * FastMath.PI;
        SphericalCoordinates sc1 = new SphericalCoordinates(2.0, 0, piO2);
        Assert.assertEquals(0, sc1.getCartesian().distance(new Vector3D(2, 0, 0)), 1.0e-10);
        SphericalCoordinates sc2 = new SphericalCoordinates(2.0, piO2, piO2);
        Assert.assertEquals(0, sc2.getCartesian().distance(new Vector3D(0, 2, 0)), 1.0e-10);
        SphericalCoordinates sc3 = new SphericalCoordinates(2.0, FastMath.PI, piO2);
        Assert.assertEquals(0, sc3.getCartesian().distance(new Vector3D(-2, 0, 0)), 1.0e-10);
        SphericalCoordinates sc4 = new SphericalCoordinates(2.0, -piO2, piO2);
        Assert.assertEquals(0, sc4.getCartesian().distance(new Vector3D(0, -2, 0)), 1.0e-10);
        SphericalCoordinates sc5 = new SphericalCoordinates(2.0, 1.23456, 0);
        Assert.assertEquals(0, sc5.getCartesian().distance(new Vector3D(0, 0, 2)), 1.0e-10);
        SphericalCoordinates sc6 = new SphericalCoordinates(2.0, 6.54321, FastMath.PI);
        Assert.assertEquals(0, sc6.getCartesian().distance(new Vector3D(0, 0, -2)), 1.0e-10);
    }

    @Test
    public void testCoordinatesCtoS() throws DimensionMismatchException {
        double piO2 = 0.5 * FastMath.PI;
        SphericalCoordinates sc1 = new SphericalCoordinates(new Vector3D(2, 0, 0));
        Assert.assertEquals(2,           sc1.getR(),     1.0e-10);
        Assert.assertEquals(0,           sc1.getTheta(), 1.0e-10);
        Assert.assertEquals(piO2,        sc1.getPhi(),   1.0e-10);
        SphericalCoordinates sc2 = new SphericalCoordinates(new Vector3D(0, 2, 0));
        Assert.assertEquals(2,           sc2.getR(),     1.0e-10);
        Assert.assertEquals(piO2,        sc2.getTheta(), 1.0e-10);
        Assert.assertEquals(piO2,        sc2.getPhi(),   1.0e-10);
        SphericalCoordinates sc3 = new SphericalCoordinates(new Vector3D(-2, 0, 0));
        Assert.assertEquals(2,           sc3.getR(),     1.0e-10);
        Assert.assertEquals(FastMath.PI, sc3.getTheta(), 1.0e-10);
        Assert.assertEquals(piO2,        sc3.getPhi(),   1.0e-10);
        SphericalCoordinates sc4 = new SphericalCoordinates(new Vector3D(0, -2, 0));
        Assert.assertEquals(2,           sc4.getR(),     1.0e-10);
        Assert.assertEquals(-piO2,       sc4.getTheta(), 1.0e-10);
        Assert.assertEquals(piO2,        sc4.getPhi(),   1.0e-10);
        SphericalCoordinates sc5 = new SphericalCoordinates(new Vector3D(0, 0, 2));
        Assert.assertEquals(2,           sc5.getR(),     1.0e-10);
        //  don't check theta on poles, as it is singular
        Assert.assertEquals(0,           sc5.getPhi(),   1.0e-10);
        SphericalCoordinates sc6 = new SphericalCoordinates(new Vector3D(0, 0, -2));
        Assert.assertEquals(2,           sc6.getR(),     1.0e-10);
        //  don't check theta on poles, as it is singular
        Assert.assertEquals(FastMath.PI, sc6.getPhi(),   1.0e-10);
    }

    @Test
    public void testGradient() {
        for (double r = 0.2; r < 10; r += 0.5) {
            for (double theta = 0; theta < 2 * FastMath.PI; theta += 0.1) {
                for (double phi = 0.1; phi < FastMath.PI; phi += 0.1) {
                    SphericalCoordinates sc = new SphericalCoordinates(r, theta, phi);

                    DerivativeStructure svalue = valueSpherical(new DerivativeStructure(3, 1, 0, r),
                                                                new DerivativeStructure(3, 1, 1, theta),
                                                                new DerivativeStructure(3, 1, 2, phi));
                    double[] sGradient = new double[] {
                        svalue.getPartialDerivative(1, 0, 0),
                        svalue.getPartialDerivative(0, 1, 0),
                        svalue.getPartialDerivative(0, 0, 1),
                    };

                    DerivativeStructure cvalue = valueCartesian(new DerivativeStructure(3, 1, 0, sc.getCartesian().getX()),
                                                                new DerivativeStructure(3, 1, 1, sc.getCartesian().getY()),
                                                                new DerivativeStructure(3, 1, 2, sc.getCartesian().getZ()));
                    Vector3D refCGradient = new Vector3D(cvalue.getPartialDerivative(1, 0, 0),
                                                         cvalue.getPartialDerivative(0, 1, 0),
                                                         cvalue.getPartialDerivative(0, 0, 1));

                    Vector3D testCGradient = new Vector3D(sc.toCartesianGradient(sGradient));

                    Assert.assertEquals(0, testCGradient.distance(refCGradient) / refCGradient.getNorm(), 5.0e-14);

                }
            }
        }
    }

    @Test
    public void testHessian() {
        for (double r = 0.2; r < 10; r += 0.5) {
            for (double theta = 0; theta < 2 * FastMath.PI; theta += 0.2) {
                for (double phi = 0.1; phi < FastMath.PI; phi += 0.2) {
                    SphericalCoordinates sc = new SphericalCoordinates(r, theta, phi);

                    DerivativeStructure svalue = valueSpherical(new DerivativeStructure(3, 2, 0, r),
                                                                new DerivativeStructure(3, 2, 1, theta),
                                                                new DerivativeStructure(3, 2, 2, phi));
                    double[] sGradient = new double[] {
                        svalue.getPartialDerivative(1, 0, 0),
                        svalue.getPartialDerivative(0, 1, 0),
                        svalue.getPartialDerivative(0, 0, 1),
                    };
                    double[][] sHessian = new double[3][3];
                    sHessian[0][0] = svalue.getPartialDerivative(2, 0, 0); // d2F/dR2
                    sHessian[1][0] = svalue.getPartialDerivative(1, 1, 0); // d2F/dRdTheta
                    sHessian[2][0] = svalue.getPartialDerivative(1, 0, 1); // d2F/dRdPhi
                    sHessian[0][1] = Double.NaN; // just to check upper-right part is not used
                    sHessian[1][1] = svalue.getPartialDerivative(0, 2, 0); // d2F/dTheta2
                    sHessian[2][1] = svalue.getPartialDerivative(0, 1, 1); // d2F/dThetadPhi
                    sHessian[0][2] = Double.NaN; // just to check upper-right part is not used
                    sHessian[1][2] = Double.NaN; // just to check upper-right part is not used
                    sHessian[2][2] = svalue.getPartialDerivative(0, 0, 2); // d2F/dPhi2

                    DerivativeStructure cvalue = valueCartesian(new DerivativeStructure(3, 2, 0, sc.getCartesian().getX()),
                                                                new DerivativeStructure(3, 2, 1, sc.getCartesian().getY()),
                                                                new DerivativeStructure(3, 2, 2, sc.getCartesian().getZ()));
                    double[][] refCHessian = new double[3][3];
                    refCHessian[0][0] = cvalue.getPartialDerivative(2, 0, 0); // d2F/dX2
                    refCHessian[1][0] = cvalue.getPartialDerivative(1, 1, 0); // d2F/dXdY
                    refCHessian[2][0] = cvalue.getPartialDerivative(1, 0, 1); // d2F/dXdZ
                    refCHessian[0][1] = refCHessian[1][0];
                    refCHessian[1][1] = cvalue.getPartialDerivative(0, 2, 0); // d2F/dY2
                    refCHessian[2][1] = cvalue.getPartialDerivative(0, 1, 1); // d2F/dYdZ
                    refCHessian[0][2] = refCHessian[2][0];
                    refCHessian[1][2] = refCHessian[2][1];
                    refCHessian[2][2] = cvalue.getPartialDerivative(0, 0, 2); // d2F/dZ2
                    double norm =  0;
                    for (int i = 0; i < 3; ++i) {
                        for (int j = 0; j < 3; ++j) {
                            norm = FastMath.max(norm, FastMath.abs(refCHessian[i][j]));
                        }
                    }

                    double[][] testCHessian = sc.toCartesianHessian(sHessian, sGradient);
                    for (int i = 0; i < 3; ++i) {
                        for (int j = 0; j < 3; ++j) {
                            Assert.assertEquals("" + FastMath.abs((refCHessian[i][j] - testCHessian[i][j]) / norm),
                                                refCHessian[i][j], testCHessian[i][j], 1.0e-14 * norm);
                        }
                    }

                }
            }
        }
    }

    public DerivativeStructure valueCartesian(DerivativeStructure x, DerivativeStructure y, DerivativeStructure z) {
        return x.divide(y.multiply(5).add(10)).multiply(z.pow(3));
    }

    public DerivativeStructure valueSpherical(DerivativeStructure r, DerivativeStructure theta, DerivativeStructure phi) {
        return valueCartesian(r.multiply(theta.cos()).multiply(phi.sin()),
                              r.multiply(theta.sin()).multiply(phi.sin()),
                              r.multiply(phi.cos()));
    }

    @Test
    public void testSerialization() {
        SphericalCoordinates a = new SphericalCoordinates(3, 2, 1);
        SphericalCoordinates b = (SphericalCoordinates) TestUtils.serializeAndRecover(a);
        Assert.assertEquals(0, a.getCartesian().distance(b.getCartesian()), 1.0e-10);
        Assert.assertEquals(a.getR(),     b.getR(),     1.0e-10);
        Assert.assertEquals(a.getTheta(), b.getTheta(), 1.0e-10);
        Assert.assertEquals(a.getPhi(),   b.getPhi(),   1.0e-10);
    }

}

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